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Evaluate the logarithm.
Round your answer to the nearest thousandth.

log_(4)(0.6)~~

◻

Evaluate the logarithm. $\newline$ Round your answer to the nearest thousandth. $\newline$ $\log _{4}(0.6) \approx$ $\newline$ $\square$

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Product property of logarithms

Full solution

Q. Evaluate the logarithm.

\newline

Round your answer to the nearest thousandth.

\newline

\log _{4}(0.6) \approx

\newline

\square

Use Calculator for Log: We need to use a calculator to find the value of $\log_{4} 0.6$ because it's not a common log base.
Change of Base Formula: On the calculator, we can use the change of base formula: $\log_{4} 0.6 = \frac{\log(0.6)}{\log(4)}$ .
Calculate Log Values: Using a calculator, we find $\log(0.6) \approx -0.2218$ and $\log(4) \approx 0.6021$ .
Divide Log Values: Now we divide $-0.2218$ by $0.6021$ to get the log base $4$ of $0.6$ .
Round to Nearest Thousandth: The division gives us approximately $-0.368$ , but we need to round to the nearest thousandth.
Round to Nearest Thousandth: The division gives us approximately $-0.368$ , but we need to round to the nearest thousandth.Rounded to the nearest thousandth, the result is $-0.368$ .

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